Begin this writing assignment with a short description (1-2 paragraphs) of what

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Begin this writing assignment with a short description (1-2 paragraphs) of what it means for V to be a vector space. What does it mean for a collection of vectors W from V to form a subspace of V? How do you test whether or not W is subspace of V? In this written homework assignment, we will look at two new definitions: Suppose we are given a vector space V and two different subspaces W1 and W2 of V. The union W1 W2 is the set of all vectors in V that belong to either W1 or W2 (or both). The intersection is the set of all vectors in V that belong to both W1 and W2. Take V to be R2, and choose two example subspaces W1 and W2 of V. Draw a picture illustrating W1, W2, Take V to be R3, and choose two example subspaces W1 and W2 of V. Draw a picture illustrating W1, W2, and (You can use Matlab, Mathematica, Wolfram Alpha, etc., to illustrate this if you are fancy enough to do that). True / false? is always a subspace of V? If the answer is "True", prove it! If not, show why not. True / false? is always a subspace of V? If the answer is "True", prove it! If not, show why not.

Explanation / Answer

question1:-

Vector Space:-

Definition: A vector space is a set V on which two operations + and

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